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The distribution of prime numbers / Dimitris Koukoulopoulos.

By: Koukoulopoulos, Dimitris, 1984- [author.].
Material type: TextTextSeries: Graduate studies in mathematics, volume 203.Publisher: Providence, Rhode Island : American Mathematical Society, [2019]Description: xii, 356 pages; USD 85.00 26 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470447540.Subject(s): Numbers, Prime | Number theory -- Instructional exposition (textbooks, tutorial papers, etc.) | Number theory -- Multiplicative number theory | Number theory -- Zeta and $L$-functions: analytic theoryDDC classification: 512.7/3 Other classification: 11-01 | 11Nxx | 11Mxx
Contents:
And then there were infinitely many -- Asymptotic estimates -- Combinatorial ways to count primes -- The Dirichlet convolution -- Dirichlet series -- An explicit formula for counting primes -- The Riemann zeta function -- The Perron inversion formula -- The prime number theorem -- Dirichlet characters -- Fourier analysis on finite Abelian groups -- Dirichlet L-functions -- The prime number theorem for arithmetic progressions -- Primes and multiplicative functions -- Evolution of sums of multiplicative functions -- The distribution of multiplicative functions -- Large deviations -- Twin primes -- The axioms of Sieve theory -- The fundamental lemma of Sieve theory -- Applications of Sieve methods -- Selberg's Sieve -- Sieving for zero-free regions -- Vinogradov's method -- Ternary arithmetic progressions -- Bilinear forms and the large sieve -- The Bombieri-Vinogradov theorem -- The least prime in an arithmetic progression -- Small gaps between primes -- Large gaps between primes -- Irregularities in the distribution of primes
List(s) this item appears in: 2020-03-06
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks
512.73 KOU (Browse shelf) Available 10794
Total holds: 0

Includes bibliographical references and index.

And then there were infinitely many -- Asymptotic estimates -- Combinatorial ways to count primes -- The Dirichlet convolution -- Dirichlet series -- An explicit formula for counting primes -- The Riemann zeta function -- The Perron inversion formula -- The prime number theorem -- Dirichlet characters -- Fourier analysis on finite Abelian groups -- Dirichlet L-functions -- The prime number theorem for arithmetic progressions -- Primes and multiplicative functions -- Evolution of sums of multiplicative functions -- The distribution of multiplicative functions -- Large deviations -- Twin primes -- The axioms of Sieve theory -- The fundamental lemma of Sieve theory -- Applications of Sieve methods -- Selberg's Sieve -- Sieving for zero-free regions -- Vinogradov's method -- Ternary arithmetic progressions -- Bilinear forms and the large sieve -- The Bombieri-Vinogradov theorem -- The least prime in an arithmetic progression -- Small gaps between primes -- Large gaps between primes -- Irregularities in the distribution of primes